A local Ford Motor Co. union has rejected a contract agreement between the company and the United Auto Workers, indicating that Ford and the UAW could have a tough time getting some workers to accept the deal.

UAW Local 900, which represents workers at three plants outside Detroit, said Tuesday that 51.1 percent of its workers voted to reject the agreement. A total of 2,582 workers voted.

Ford and the UAW reached a tentative agreement on the four-year contract last week, but workers must ratify it. Local 900 was one of the first to vote on the agreement. More votes are scheduled later this week and into next week.

Under the agreement, most workers will get profit-sharing checks instead of annual raises. Workers also would get a $6,000 signing bonus and the promise of thousands of new jobs in U.S. plants through 2015. The contract promises a new shift with 1,400 workers for the Michigan Assembly Plant, which is represented by Local 900.

The agreement is more generous than the new contract for General Motors Co. workers, who approved their deal last month by a wide margin. Chrysler Group LLC and the UAW are still negotiating.

Bill Johnson, the bargaining chairman of the Michigan Assembly Plant, which makes the Ford Focus, said workers are angry that the contract doesn’t give back some of the things they lost in previous agreements, including annual raises, cost-of-living increases and additional holidays. He said they’re also mad about Ford CEO Alan Mulally’s $26.5 million pay package for 2010.

“People are jittery. They’re just scared,” Johnson said.

But local politics also played a role. The agreement would cut back on overtime pay at the plant because new workers would be hired, for example. Johnson didn’t sign a letter from other Local 900 leaders endorsing the agreement.

The UAW said Tuesday that a small majority of workers are supporting the deal so far. With 7 percent of local unions voting, 50.1 percent of production workers have approved the contract, the union’s Ford department said on its Facebook site.

A simple majority of voting members is needed for the contract’s adoption at Ford.